 IvyWise Resources

# Five Helpful Calculator Skills for the AP Calculus Exam By Kaitlyn, IvyWise Master Tutor

You’ve spent all year working hard and mastering the difficult topics covered in AP Calculus. The AP exam is just around the corner and you want to be as prepared as possible. The exam is broken into two sections: Multiple Choice and Free Response. You will have access to your calculator for a total of 17 questions: 15 Multiple Choice and 2 Free Response. It is so important to know how to properly use your graphing calculator so that you can maximize your resources and let your brain take a little break from difficult calculations. Here are five skills that you should have mastered before you begin your exam this spring.

## Skill 1: Calculate a Derivative

A Free Response question might ask you to find the derivative of a function at a specific value and then interpret what the derivative means in the context of the problem. If you have a calculator available, use it from the very beginning. Do not calculate the derivative by hand and then use your calculator to plug the value in. One very common mistake that hurts a student’s score is trying to work out a complex problem by hand when a calculator is available!

Example AP Exam Question:

During the time interval 0 ≤ t ≤ 2, the total number of people at a concert arena can be modeled by the function M(t) = 960sin(0.2t2 + 3t + 2), where t is measured in hours. Assume that nobody leaves the arena during the time interval. Determine the value of M′(1). Using correct units, interpret the meaning of your answer in the context of this problem.

## Skill 2: Calculate an Integral

Understanding integrals is essential for success on the AP Exam. When a problem involving total amounts or average value is asked on the AP Exam, an integral is needed. Similar to the derivative problems, if a calculator is available, do not do any of the math out by hand. What the AP graders will be looking for is an integral set up with the correct notation, so make sure to do that, but then let the calculator do the rest of the work for you.

Example AP Exam Question:

Suppose that the rate of water flow is approximated by R(t) = 0.03(760 + 30x – 4x2), where R(t) is measured in gallons per hour and is measured in hours. Use R(t) to approximate the average rate of water flow during a 24-hour period. Indicate units of measure.

## Skill 3: Graph a Derivative

The graphs of the first and second derivatives can give you so much information about the function itself, such as maximums, minimums, intervals of increasing, intervals of decreasing, points of inflection, and intervals of concavity. Rather than calculating the derivative by hand and algebraically finding critical values, use your graphing calculator to graph the derivative and use that graph to help you answer the problem at hand.

Example AP Exam Question:

Let f'(x) = (lnx)/(4x− sin x for 1 < x < 6. On what intervals is f concave up?

1. (3.127, 6)
2. (1.569, 4.710)
3. (1, 1.569)
4. (4.710, 6)

## Skill 4: Graphically Find the Solution to an Equation

A common Free Response question is to find the area between two curves. In order to solve this type of problem, you will need to know where those two curves intersect. This should be done on your calculator. Graph each equation and find where they intersect. The graphing calculator can also help you find the actual area of those regions by calculating the integrals for you.

Example AP Exam Question:

Let f (x) = 2 + x + ex2 −6x and g(x) = x4 − 8.5x2 + 9.5x + 3. Let R and S be the two regions enclosed by the graphs of f and g. Find the sum of the areas of regions R and S.

## Skill 5: Use the Equation Solver

Your graphing calculator has an equation solver built into it. You can use this feature any time you need to find the solution to an equation.

Example AP Exam Question:

Let f  be the function given by f (x) = 5e2x+3 and let g be the function given by g(x) = -8x2 − 5x − 7. At what value of x do the graphs of f and g have parallel tangent lines?

1. –1.446
2. -1.281
3. -1.062
4. -0.997

## Other Helpful AP Calculus Exam Tips:

• Make sure your calculator is fully charged or has fresh batteries before your AP Exam. You are allowed to bring two calculators to the exam in case something happens to one of them. Check the College Board website for a list of approved calculators.
• Your calculator should be in radian mode. To check, hit the mode button on your calculator. There are two modes for angles: degrees and radians. Make sure that radians is selected.
• Do not round until the final answer. Use the Ans button if you need to do multi-step calculations. When you are ready to round, round to three decimal places.
• Do not be afraid to do entire problems out on your calculator, with little to no algebraic manipulation done by you. However, on Free Response questions, Calculus must be used to justify a response. If a question asks for a relative maximum or minimum, although this can be found on the calculator, no points will be awarded if Calculus is not used to justify the answer. Also, correct Calculus notation must be used on Free Response questions, not the notation that is typed into the calculator.

There’s a lot that goes into preparing for AP exams, and the team of expert tutors here at IvyWise can help you reach your goal score through personalized test prep and tutoring. For more information on how we can help you get ready for the AP Calculus exam, or any other AP exam, contact us today!